There is the house edge providing positive expected value to investors, just like dividends for stocks. Investors however are less concerned of dividend risk, but on total return of capital after the investment is sold.
The line between an investor and gambler is blurred, but there are some levels of risk appetite typical for them. Investments have annualized return volatilities of roughly 1-10% for bonds 10-40% for blue chips, a return volatility above 100% is rather gambling.
Assuming gambler on JD play >50.5%, then the volatility is proportional to Sqrt[n*0.505*0.495] for n rolls.
An investor into the site has an annualized volatility of return of about betsize/bank*Sqrt[betsperyear*0.505*0.495].
Note that with varying bet size or bets other than >50.5% the volatility increases, therefore next calculations are lower limits of the actual volatility.
The expected number of bets per year extrapolated form today's stat is: 521890, the average bet size before Nakowa were: 8.1 BTC, bankroll was around 50,000.
An investor faced annualized return volatility of at least 5.8%.
After Nakowa the average bet size is: 90.1 and bankroll is 30,000 that leads to at least 108% return volatility.
Investors are gamblers now, therefore I disinvested until doog reduces the max bet size with a magnitude.
Interesting. Thanks for posting this.
But I wonder, isn't reducing max betsize only a moderately effective solution? Say *max bet size* is reduced to a tenth of its previous value, but as a result *number of bets increases tenfold* (not completely unlikely). Then, according to your formula, return volatility is reduced only by a factor of about 3 (/10, *sqrt(10)).
The return is dominated by the binomial distribution but modified with varying bet size and varying p for which distribution is unknown The lower limits of risk (aka. volatility) I calculated are assuming pure binomial.
Yes, the return volatility within the same timeframe increases with increasing number of bets (n), proportional to sqrt(n).
The expected return (out of house edge) increases proportional to n and proportional to bet size.
People use annualized volatility to be able to compare risk of things that are influenced by events of different frequency or over different time horizon.
See
http://en.wikipedia.org/wiki/Binomial_distribution Hints: volatility is the square root of statistical Variance. Statistical Mean is the expected return out of house edge.
